Syllabus updated January 22, 2009.

Basic course info

Grades and duties

Course Outline

Texts

Course Description

Introduction:

Combinatorics is the study of counting the number of elements in a finite set.  Much of mathematics could be described in this way, but enumerative combinatorics has been formalized and unified over the last 50 years, based on motivation from computer science.  This focus has brought coherence and unity to the subject. 

This course teaches concepts, methods and models of counting and estimation that are essential for any discrete mathematician and are valuable for researchers in algebra, statistics, computer science, computer engineering and other scientific fields.
 

Grades and Duties

Grades will be determined by the following items:

1. Homework 1, due February 3. (20 pts.)
2. Homework 2, scheduled to be due February 17. (20 pts.)
3. Homework 3, scheduled to be due March 24. (20 pts.)
4. Homework 4, scheduled to be due April 10. (20 pts.)
5. Homework 5, scheduled to be due April 21 (20 pts.)
6. Take-home midterm exam, scheduled to be due March 5. (50 pts.)
7. Take-home final exam, due date TBA. (50 pts.)

Exams: The midterm exam will cover first-half topics and the final exam will cover second-half topics only. The exams will be take-home exams.  The midterm exam will be assigned the previous Tuesday.  So it is due in about 46.5 hours.  The final exam timetable will be announced in class and on the main page. Students may not work with anyone else on a take-home exam.

Homework assignments: These problems will be distributed one week before the due date and will be posted on the archive page. Students may discuss homework but must submit their own writeup which should represent their own work.  You may discuss problems with me in office hours.  I will help you, but you cannot take notes in my office Solutions must be typed. You may submit them electronically if you wish. If you are planning to give a seminar talk this semester in any related seminar (see Discrete Math seminar or Algebra seminar, for example) you can be excused from one homework assignment. See me first.  You may pick whichever homework you want to skip, but it must be chosen before it is distributed. If you do not wish to speak at a seminar, you can give a talk in class instead to be excused from one homework.  The talk should be 40 minutes and would be given during dead week.  Again, please see me first.

The main course page at http://orion.math.iastate.edu/rymartin/ISU606/ISU606.shtml will have updates as well as a general outline for the course.

Preliminary Course Outline:

• Week 1 topics: Useful inequalities, Stirling's formula.
• Week 2 topics: Compositions, multisets, permutations.
• Week 3 topics: Permutations, partitions, the twelvefold way.
• Week 4 topics: Stirling numbers, sieve methods
• Weeks 5-8 topics: Generating functions
• Weeks 9-12 topics: Partially ordered sets, the four functions theorem
• Weeks 13-15 topics: Extremal combinatorics, TBA

Texts: There is no formal textbook for the course. I will cull my notes from a number of texts.